1. Field
The present disclosure relates to coherent detection of pulse position modulated signals. More particularly, the present disclosure describes a top-hat pulse generator (THPG) comprising polarization maintaining fiber in a nonlinear optical loop mirror, where the THPG is suitable for use in a system for the detection and demodulation of pulse position modulated optical pulses.
2. Description of Related Art
Many satellite and terrestrial optical communication systems require transmission of analog optical signals. The straightforward way to address this need is to modulate the amplitude of an optical carrier. This approach, however, suffers from poor signal-to-noise ratio (SNR). It is well known that broadband modulation techniques, which utilize higher bandwidth than that of the transmitted waveform, may improve SNR over that achieved with amplitude modulation. Pulse Position Modulation (PPM) is one of these techniques. In PPM, a temporal shift in the pulse position represents a sample of the transmitted waveform. The improvement in SNR near the Nyquist sampling frequency of a pulse position modulated signal over an amplitude modulated signal is shown below:SNRppm∝SNRam(tp/τ)2  Eq. (1)where tp is the temporal spacing between unmodulated pulses and τ is the pulse duration.
Conventional detection or demodulation of analog PPM optical signals, though, suffers from poor SNR at low frequencies. PPM signals are usually demodulated from the optical to electronic domain by a photodiode followed by a lowpass filter (LPF) that converts pulse position modulation to amplitude modulation. Such a demodulation technique is not capable of recovering the DC component, since the DC component is represented by a constant temporal shift of all pulses from their unmodulated positions. Moreover, the demodulated signals after the lowpass filter have very low amplitude at low frequencies. The amplitude increases linearly with frequency up to the Nyquist limit. Such frequency-dependent distortion is corrected by an integration circuit, which amplifies low-frequency noise accordingly, resulting in decreased SNR performance.
An apparatus and method for detecting an optical PPM signal are described in U.S. Pat. No. 6,462,860, herein incorporated by reference. FIG. 1 depicts an optical receiver 50 that detects optical pulse position modulated signals and converts the detected pulses to an electrical waveform according to the general disclosure of U.S. Pat. No. 6,462,860. The optical receiver 50 receives both short optical clock pulses 11 and short pulse position modulated optical pulses 21. The short optical clock pulses 11, which have a fixed period, are converted to rectangular clock pulses 13 by, preferably, a top hat generator 10. Short optical signal pulses 21 are converted to rectangular pulses 23 by another top hat generator 20. An overlap-to-electric converter 30 detects the amount of overlap 33 between the rectangular clock pulses 13 and the rectangular signal pulses 23 and converts the overlap amount 33 into an electrical signal. The overlap amount is a measure of the delay between the optical clock pulses 11 and the pulse position modulated signal pulses 21. The overlap-to-electric converter 30 may comprise a coherent correlator, a sum frequency generator, a four-wave mixer, or other means that can measure the amount of overlap between separate streams of rectangular pulses and output the measured amount as an electrical signal.
As noted above, overlap to electric conversion may be achieved by any of several methods known in the art. For example, an exemplary coherent correlator 140 is shown in FIG. 4A and is described in additional detail below, in relation to the circuit depicted in FIG. 2. The overlap-to-electric converter 30 may also comprise a sum frequency generator or a four-wave mixer. Sum frequency generators are well-known in the art. An exemplary sum frequency generator is depicted in FIG. 4B and is described in additional detail below. An exemplary four-wave mixing apparatus is depicted in FIG. 4C and is described in additional detail below. However, those skilled in the art will understand that additional methods and apparatus may be used to provide overlap to electric conversion.
The apparatus and method for detecting an optical PPM signal described in U.S. Pat. No. 6,462,860 discloses the use of a coherent correlator for an overlap-to-electric converter. FIG. 2 depicts an embodiment of an optical receiver 100 described in U.S. Pat. No. 6,462,860, which uses a coherent correlator. In FIG. 2, a first top-hat generator 110 receives a pulse position modulated optical signal Psig(λsig) and a continuous wave optical signal CW(λCW), and produces a rectangular signal pulse output RPsig(λCW). Still referring to FIG. 2, a second top-hat generator 120 receives a pulse optical clock Pclk(λclk) and the continuous wave optical signal CW(λCW), and produces a rectangular clock pulse output RPclk(λCW). A continuous wave source 130 provides the continuous wave optical signal CW(λCW). Depending upon the chosen architecture of the correlator 140, a single CW source 130 or a pair of distinct CW sources may be used. If a pair of distinct CW sources are used the CW sources may either generate on the same or on different wavelengths, again depending upon the architecture of the correlator 140. An optical pulse source (not shown) provides the pulse optical clock signal Pclk(λclk) such that the optical pulses in the pulsed optical clock signal Pclk(λclk) are preferable equally spaced or nearly equally spaced in time. Optical pulse sources providing pulsed optical signals are known in the art. The PPM optical signal Psig(λsig) and the pulsed optical clock signal Pclk(λclk) may have the same or different optical wavelengths. In the embodiment depicted in FIG. 2, the rectangular pulse output RPsig(λCW) and the rectangular clock pulse RPclk(λCW) are synchronized and are coherent since both derive their optical frequency and phase from that of a single continuous-wave source 130.
Still referring to FIG. 2, a coherent correlator 140 receives the rectangular signal pulse output RPsig(λCW) and the rectangular clock pulse output RPclk(λCW) and produces a current output Is(t) 74. The output Is(t) 74 of the coherent correlator 140 is proportional to the cross-correlation product of the rectangular signal pulse output RPsig(λCW) and the rectangular clock pulse output RPclk(λCW). This cross-correlation product is also proportional to the offset in time between each PPM pulse and its corresponding clock pulse. Thus, the output of the coherent correlator 140 provides a demodulated analog signal corresponding to the original analog pulse position modulated signal.
The top-hat generators 110, 120 shown in FIG. 2 preferably each comprise a nonlinear optical loop mirror (NOLM) with a control input. NOLMs are well known in the art and can be constructed by splicing together commercial fibers and couplers. U.S. Pat. No. 5,208,455, issued to B. P. Nelson et al. on May 4, 1993, describes the construction of a typical nonlinear optical loop mirror. Non-linear optical loop mirrors are also further described by S. Bigo, O. Leclerc, and E. Desurvire in “All Optical Fiber Signal Processing and Regeneration for Soliton Communications,” IEEE J. Sel. Topics Quant. Electron., Vol. 3 (1997), p. 1208.
FIG. 3 depicts a typical NOLM 500 with a control input. The NOLM 500 comprises a first coupler 510 for coupling a continuous wave optical signal OPTCW into the NOLM 500 and a second coupler 520 for coupling an optical control pulse OPTCP into the NOLM 500. The optical loop of the NOLM is formed by an optical fiber 550 that is routed from one branch of the first coupler 510 to another branch of the first coupler 510. A filter 560 may be disposed at another branch of the first coupler 510 to filter out signals at the optical wavelength of the optical control pulse, while allowing signals at the optical wavelength of the continuous wave optical signal to pass from the NOLM 500.
Returning to FIG. 2, the one or two frequency continuous wave sources 130 operating at optical wavelengths λ1,2CW feed into the top-hat generators 110, 120 comprising NOLMs. Both NOLMs are preferably completely symmetrical so that the continuous wave radiation is reflected completely in the absence of control radiation. The signal and clock pulses at wavelengths λsig and λclk, act as control signals in the first and second NOLMs respectively. For the NOLMs to operate correctly, the wavelengths of the control signals λsig and λclk must be different than that of the continuous wave radiation at λCW. If properly configured, the NOLMs preferably provide pulses with top-hat temporal shapes.
As shown in FIG. 2, the trains of rectangular signal RPsig(λCW) and clock RPclk(λCW) pulses at the continuous wave frequency λCW (or frequencies (λ1,2CW)) are combined in the optical correlator 140. For example, the optical correlator 140 may comprise a 3 dB coupler 141 and a balanced detector 143, as shown in FIG. 4A. In this case, the pulse and signal trains are preferably on the same wavelength and coherent, as is well known in the art. The electric current of the correlator 140 is given by:
                    I        =                              ∫                          -              ∞                        ∞                    ⁢                                                    E                sig                            ⁡                              (                                  t                  -                                      Δ                    ⁢                                                                                  ⁢                    t                                                  )                                      ⁢                                          E                clk                            ⁡                              (                t                )                                      ⁢                          ⅆ              t                                                          Eq        .                                  ⁢                  (          2          )                    where Δt is the temporal shift between the signal and control pulses and Esig,clk(t) is the temporal shape of the rectangular pulses.
FIG. 5 shows the relationship between the input optical clock pulses 11 and the pulse position modulated signal pulses 21 and the correlator current 74 produced by the optical correlator 140 depicted in FIG. 2. As shown in FIG. 5, the greater the overlap 33 between the rectangular clock pulses 13 and the rectangular signal pulses 23, the greater the correlator current 74 produced by the optical correlator 140. Of course, as noted above, devices other than an optical correlator may be used to detect the overlap 33 and to output an electrical signal based on the overlap.
As briefly mentioned above, an optical correlator is one way to provide the overlap-to-electric converter used in embodiments of the present invention. However, a sum frequency generation apparatus 440, as shown in FIG. 4B, may also be used. Such circuits are well known in the art. The sum frequency circuit 440 comprises a lens 441 for focusing beams comprising the top-hat pulses of the clock THclk 446 and the signal THsig 447 into a non-linear crystal 443. The non-linear crystal may comprise lithium niobate. The two beams 446, 447 are directed through the non-linear crystal 443, where they produce sum-frequency beam 448, which propagates within the sector between the two beams 446, 447 to an aperture 445. The sum-frequency radiation is generated only when the clock pulses and the signal pulses overlap in time. Therefore, the electric current from the photodetector 449 is proportional to the amount of overlap. To increase the efficiency of the sum-frequency correlator, a waveguiding Periodically Poled Lithium Niobate (PPLN) device (available, for example, from Lightbit) may be used. In this case, rectangular signal and clock pulses are preferably on different wavelengths, which call for two distinct CW sources for the corresponding NOLMs.
Four-wave mixing may also be used to provide the required overlap to electric conversion. FIG. 4C depicts a four-wave mixing apparatus well known in the art. The top-hat pulses of the clock THclk at a wavelength ωclk and the signal THsig at a wavelength ωsig are directed into a single mode fiber 450, which is, preferably, a dispersion shifted fiber. Preferably, the length of the fiber should be below the fiber dispersion length for the top-hat pulses. Four-wave mixing occurs within the fiber 450 to produce a signal at a wavelength ω4F=2ωclk−ωsig or ω4F=2ωsig−ωclk. A photodetector may then be used to detect and convert the four-wave output signal to an electric signal that is proportional to the overlap between the clock and signal pulses.
In the embodiment shown in FIG. 2, the rectangular pulse created by a specific PPM pulse should not overlap the rectangular pulse created by a clock pulse for a preceding or a following PPM period. Therefore, the maximum temporal shift for PPM pulses ΔtPmax is preferably smaller than the duration of the rectangular pulses tTH created by the top-hat pulse generators, and the sum of the two values, ΔtPmax+tTH, is preferably less than tp, the interval between the clock pulses. Hence, ΔtPmax<tp/2, so the PPM signal preferably has a modulation index M of less than 0.5. Therefore, the individual pulses of the PPM signal are shifted from their non-modulated positions of Δt=±tp/4 within the time slot of−tp/4<Δt<tp/4.
The linearity of an optical PPM receiver using top-hat pulse generators, whether using the coherent detection technique described above and shown in FIG. 2 or other techniques or apparatus, typically depends on the quality of the rectangular pulses generated by the top-hat pulse generators. The quality of the rectangular pulses is essentially the closeness of the shape of the generated pulses to a true “top-hat” shape. When a NOLM is used to generate the rectangular pulse, the control pulse, which imprints a non-linear phase shift on the co-propagating CW beam as described above, should preferably retain its shape along the whole length of the NOLM. Therefore, in the type of optical PPM receivers shown in FIGS. 1 and 2 and disclosed in U.S. Pat. No. 6,462,860, the performance of those optical PPM receivers improves as the shapes of the optical pulses provided by the NOLMs more closely approach a true top-hat shape.
In U.S. Pat. No. 6,462,860, a NOLM comprising a fiber having a dispersion that is zero at the wavelength of the control pulse, either signal or clock, is discussed. The control pulse maintains its shape due to the zero dispersion fiber. The result is increased linearity over a conventional NOLM, which provides for a more top-hat shaped pulse. However, this restriction on fiber dispersion may be hard to meet, since most commercial-off-the-shelf fibers do not have this capability. Moreover, even if such fibers are readily available, the control pulse would still suffer some shape degradation due to higher-order dispersion and self-phase modulation.
Instead of special zero dispersion fibers, a NOLM controlled with an optical soliton control pulse may also provide a more linear NOLM than a conventional NOLM. It is well known in the art that optical solitons preserve their temporal shape during propagation. Since the control pulse retains its shape (due to its soliton nature) as it slides along the co-propagating CW beam, a constant nonlinear phase shift is imprinted on the CW beam by the control pulse along the length of their overlap. This constant phase shift assures a flat top of the top-hat pulse at the NOLM output. U.S. patent application Ser. No. 10/341,689 titled “An Optical Top Hat Pulse Generator” and filed Jan. 13, 2003, incorporated by reference herein in its entirety, discloses such a soliton-based NOLM.
If a NOLM is controlled with a soliton control pulse, the output of the NOLM comprises an optical pulse output that has a leading edge, a trailing edge and intermediate plateau that provides for a true “top-hat” shape. Hence, optical PPM receivers using NOLMs that are controlled by first order solitons should provide more linear performance.
When using first order solitons to control a NOLM, the NOLM should comprise a fiber with positive dispersion (in ps/nm×km), which supports optical solitons. The soliton regime for the control pulse is achieved by (i) choosing a fiber with the correct, i.e., positive, dispersion sign (that is,
            D      =              -                              2            ⁢                                                  ⁢            π            ⁢                                                  ⁢            c                                λ            2                                ,                  β        2            >      0        )and (ii) adjusting the peak power of the control pulse inside the loop to that of the first order soliton, as shown below
                              P          c                =                                                                          β                2                                                                  γ              ⁢                                                          ⁢                              t                0                2                                              =                                                    3.11                ⁢                                                                        β                    2                                                                                                γ                ⁢                                                                  ⁢                                  t                  FWHM                  2                                                      =                                          3.11                ⁢                                                                  ⁢                                  λ                  2                                ⁢                D                                            2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                c                ⁢                                                                  ⁢                γ                ⁢                                                                  ⁢                                  t                  FWHM                  2                                                                                        Eq        .                                  ⁢                  (          3          )                    where γ≈1.5–10 W−1/km is the non-linear fiber constant, tFWHM=2 ln(√{square root over (2)}+1)t0 is the optical pulse duration (full width half maximum), c is the speed of light and D is the fiber dispersion in ps/nm/km. Also, in equation (3), β2 is the fiber dispersion (in s2/cm) at the wavelength λ of the control pulse.
The peak output power of a top-hat pulse generator controlled by optical solitons may be calculated as follows:pTHpeak=PCW sin2(φNLmax)  Eq. (4)where PCW is the power of the CW beam feeding the NOLM. φNLmax is the non-linear phase shift of the CW beam that co-propagates with the control pulse and may be calculated as follows:
                                          φ            NL            max                    ⁡                      (            t            )                          =                  C          ⁢                                    δ              ⁢                                                          ⁢                              λ                FWHM                                                    Δ              ⁢                                                          ⁢              λ                                                          Eq        .                                  ⁢                  (          5          )                    where δλFWHM=(2 ln(√{square root over (2)}+1)/π2)λ2/tFWHMc is the bandwidth of a transform-limited (sech2) pulse of tFWHM duration, Δλ is the de-tuning of the control pulse from the CW beam that feeds the NOLM, and C=3.56 and 1.19 for the same and orthogonal polarizations of the control pulse and CW beam, respectively.
G. P. Agraval, Nonlinear Fiber Optics (Academic Press, New York, 1995) provides the background for calculating the phase shift acquired by the CW beam via cross-phase modulation (XPM). The phase shift is determined by solving the standard nonlinear coupling equations
                                                        ∂                              A                CW                                                    ∂              z                                +                                    1                              v                CW                                      ⁢                                                  ⁢                                          ∂                                  A                  CW                                                            ∂                t                                                    =                  ⅈ          ⁢                                          ⁢          γ          ⁢                                          ⁢          C          ⁢                                                                  A                p                                                    2                    ⁢                      A            CW                                              Eq        .                                  ⁢                  (                      6            ⁢            a                    )                                                                            ∂              Ap                                      ∂              z                                +                                    1                              v                p                                      ⁢                                                  ⁢                                          ∂                                  A                  p                                                            ∂                t                                              +                                    ⅈ              2                        ⁢                          β              2                        ⁢                                                            ∂                  2                                ⁢                                  A                  p                                                            ∂                                  t                  2                                                                    =                  ⅈ          ⁢                                          ⁢          γ          ⁢                                          ⁢          C          ⁢                                                                  A                p                                                    2                    ⁢                      A            p                                              Eq        .                                  ⁢                  (                      6            ⁢            b                    )                    where Ap,CW are amplitudes of control pulses and CW components, C=2, ⅔ for same and orthogonal polarizations, respectively, and β2=−(2πc/λ2)D is fiber dispersion. The dispersion for the CW component is zero, i.e. β2(λCW)=0, and the XPM of a strong control pulse by a weak CW is negligible. In addition, the fast-oscillating cross-modulation term normally present is also not shown, as the term averages out over any significant distance, such as several wavelengths, i.e. a small fraction of a mm. Eq. (6b) is not coupled to Eq. (6a) and can be solved separately. For β2<0, i.e., for positive D, Eqs. (6a) and (6b) provide well-known soliton solutions as shown in Chapter 5 of G. P. Agraval, Nonlinear Fiber Optics (Academic Press, New York, 1995). One skilled in the art will appreciate that the power of the control pulse is equal to that of the fundamental soliton that retains its shape as it propagates along the fiber:
                              A          p                =                                            P              0                                ⁢          sec          ⁢                                          ⁢                      h            (                                          t                -                                  z                                      v                    p                                                                              t                0                                      )                    ⁢                                          ⁢                      ⅇ                                          ⅈ                ⁢                                                                  ⁢                z                                            2                ⁢                                                                  ⁢                                  L                  D                                                                                        Eq        .                                  ⁢                  (          7          )                    where
                              P          0                =                                                            λ                2                                            2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                c                                      ⁢                                                  ⁢                          D                              γ                ⁢                                                                  ⁢                                  t                  0                  2                                                              =                                                    λ                2                                            2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                c                                      ⁢                                                  ⁢                                                            3.11                  ⁢                  D                                                  γ                  ⁢                                                                          ⁢                                      t                    FWHM                    2                                                              .                                                          Eq        .                                  ⁢                  (          8          )                    Substituting Eq. (7) into Eqs. (6a) and (6b) and integrating the latter provides:
                                          φ            NL                    ⁡                      (                          z              ,              t                        )                          =                                                            CP                0                            ⁢              γ              ⁢                                                          ⁢                              t                0                                                                    V                cw                                  -                  1                                            -                              v                p                                  -                  1                                                              [                                    th              (                                                (                                      t                    -                                          z                                              v                        p                                                                              )                                                  t                  0                                            )                        -                          th              (                                                (                                      t                    -                                          z                                              v                        cw                                                                              )                                                  t                  0                                            )                                ]                                    Eq        .                                  ⁢                  (          9          )                    
The maximum phase shift is
                              φ          NL          max                =                  4          ⁢                                                    P                0                            ⁢              γ              ⁢                                                          ⁢                              t                0                                                                    v                cw                                  -                  1                                            -                              v                p                                  -                  1                                                              ⁢                                          ⁢          and          ⁢                                          ⁢                      4            3                    ⁢                                          ⁢                                                    P                0                            ⁢              γ              ⁢                                                          ⁢                              t                0                                                                    v                cw                                  -                  1                                            -                              v                p                                  -                  1                                                                                        Eq        .                                  ⁢                  (          10          )                    for equal and orthogonal polarizations, respectively. Eq. (10) may be further simplified for non-polarization maintaining fibers that dictate the use of small detuning between the CW and control pulsed radiations.
                                                        v              cw                              -                1                                      -                          v              p                              -                1                                              ≈                                    (                                                λ                  cw                                -                                  λ                  p                                            )                        ⁢                          ⅆ                              ⅆ                λ                                      ⁢                                                  ⁢                          1              v                                      =                  D          ⁢                                          ⁢          Δ          ⁢                                          ⁢                      λ            .                                              Eq        .                                  ⁢                  (          11          )                    Taking into account that for the fundamental solitons nonlinear and dispersion lengths are equal, we get
                                                                        P                0                            ⁢              γ                        ≡                          1                              L                NL                                              =                                    1                              L                D                                      =                                                            λ                  3                                                  2                  ⁢                  π                  ⁢                                                                          ⁢                  c                                            ⁢                                                3.11                  ⁢                                                                          ⁢                  D                                                  t                  FWHM                  2                                                                    ,                            Eq        .                                  ⁢                  (          12          )                    and Eq. (10) is modified to
                                                                        φ                NL                max                            =                            ⁢                              C                ⁢                                                      λ                    2                                                        2                    ⁢                    π                    ⁢                                                                                  ⁢                    c                                                  ⁢                                  1                                      Δ                    ⁢                                                                                  ⁢                    λ                    ⁢                                                                                  ⁢                                          t                      0                                                                                                                                              =                            ⁢                              C                ⁢                                  π                                      4                    ⁢                                                                                  ⁢                                          ln                      ⁡                                              (                                                                              2                                                    +                          1                                                )                                                                                            ⁢                                                      λ                    FWHM                                                        Δ                    ⁢                                                                                  ⁢                    λ                                                                                                                          =                            ⁢                              3.56                ⁢                                                      λ                    FWHM                                    Δλ                                ⁢                                                                  ⁢                and                ⁢                                                                  ⁢                1.19                ⁢                                                      λ                    FWHM                                    Δλ                                                                                        Eq        .                                  ⁢                  (          13          )                    for equal and orthogonal polarizations, respectively, where λFWHM is the bandwidth of a transform-limited, sech2 pulse with duration tFWHF=2 ln(√{square root over (2)}+1)t0.
The top-hat pulse generator described in U.S. patent application Ser. No. 10/341,689, while providing a more linear version of a top-hat pulse generator than others known in the art, has limited conversion efficiency. The peak output power for the top-hat pulse generator controlled by optical solitons discussed in U.S. patent application Ser. No. 10/341,689 is shown belowPTHpeak=PCW sin2(φNLmax)  Eq. (14)where PCW is the power of the CW seed and φNLmax is the non-linear phase shift of the CW beam that co-propagates with the control pulse. Thus, conversion efficiency can be calculated by
                              conversion          ⁢                                          ⁢          efficiency                =                              P            TH            peak                                P            CW            peak                                              Eq        .                                  ⁢                  (          15          )                    where PTHpeak=PTH sin2(φNLmax) and PCWpeak=PCW sin2(φsolmax)
Eqs. (5), (14) and (15) illustrate that the non-linear phase shift, and therefore, the output power and conversion efficiency for non-polarization maintaining fibers are determined by the relative de-tuning Δλ/∂λFWHM. The relative de-tuning is preferably chosen to be relatively large to prevent the control power from leaking into the output.
For example, in the design described in U.S. patent application Ser. No. 10/341,689, the choice of the relative detuning factor may depend on the amount of cross talk between the control pulse and the top-hat pulse output from the top-hat pulse generator. If the cross talk factor is allowed to exceed 2×10−3, the conversion efficiency is 0.45. If cross talk factor is improved to 10−4, the conversion efficiency decreases to 0.39. However, for communication purposes, the cross-talk factor should be several orders of magnitude less than 10−4. Measurements have shown that the minimal de-tuning for orthogonal polarizations is ≈Δλ/∂λFWHM=7.5 to achieve acceptable performance, with minimal de-tuning for some polarizations being much higher. As a result, φNLmax≦0.16 and peak conversion efficiency PTHpeak/PCW=0.025 for conventional NOLMs.
As described above, optical pulse generators that provide top-hat shaped optical pulses are known in the art, but these generators generally exhibit limited linearity and conversion efficiency. Further, U.S. application Ser. No. 10/341,689 discloses a top-hat generator that may use commercially available parts, but the disclosed system and method, while providing improved linearity, still has limited conversion efficiency. Therefore, there exists a need in the art for an optical pulse generator that can generate optical pulses with a top-hat shape with improved conversion efficiency and linearity.